This invention relates generally to digital communication systems which employ forward error correction (FEC) coding. More specifically, the present invention relates to a receiver in such a system where a quantized, soft decision data value is used in decoding the FEC coding.
Digital data communication systems may utilize any of several different transmission schemes. In one such scheme data is communicated using non-differentially encoded quadrature-PSK. In this scheme digital data at a transmitter of the system is first convolutionally encoded. The convolutional encoding increases the number of binary symbols required to carry the same information as is contained in the digital data prior to encoding, but allows a decoder at a receiver portion of the system to detect and correct errors.
Encoded data are separated into two bit pairs called symbols. The transmitter modulates a carrier signal in a manner defined by the symbols. In quadrature-PSK the carrier has in-phase (I) and quadrature (Q) components. Each bit of a symbol modulates one of the I or Q carrier components so that at the transmitter only one of four possible phase relationships exists between the I and Q components.
The information contained in the symbol-modulated carrier invariably becomes corrupted by noise in the transmission channel. Additive Gaussian noise typically describes the corruption which occurs to the carrier. FIG. 1A shows the Gaussian probability distribution function. The vertical axis of FIG. 1A describes the probability that noise of a given magnitude will occur. The horizontal axis represents the noise magnitude. Thus, a greater probability exists that low magnitude noise will affect the symbol-modulated carrier, but a finite probability exists that a large magnitude noise signal will be added to the symbol-modulated carrier.
When this symbol-modulated carrier is received by a receiver portion of the system and demodulated, a structure is provided to decide what symbol was transmitted in spite of the fact that the received symbol invariably has been corrupted by noise. FIG. 1B illustrates the problem addressed by this structure. FIG. 1B shows a 2-dimensional vector space defined by axes I and Q, where I and Q represent the in-phase and quadrature components of a received carrier. For quadrature-PSK communication, in which each symbol contains 2 bits of information, the transmitter modulates the carrier to produce only one of four possible transmitted vectors. This transmitted vector is centrally located in one of four quadrants. The four quadrants are defined in FIG. 1B so that if quadrant 0 resides from 0.degree.-90.degree. counterclockwise from the I axis, then quadrant 1 resides from 90.degree.-180.degree., quadrant 3 resides from 180.degree.-270.degree., and quadrant 2 resides between 270.degree.-360.degree.. The quadrant number reflects the symbol value which modulates the carrier. For example, as shown in FIG. 1B both the I and Q components of the carrier are positively modulated and the transmitted vector shown in phantom, which is located in quadrant 0, results. Thus, a symbol of 00 is being communicated. On the other hand, if the I component were negatively modulated while the Q component were positively modulated then the resulting transmitted vector would reside in quadrant 1 and a symbol of 01 would be communicated.
The additive Gaussian noise which corrupts the transmitted symbol is illustrated in FIG. 1B by concentric circles centered at the coordinates for each of the four possible transmitted vectors. A greater probability exists that low magnitude noise will add to the transmitted vector, but a distinct finite probability exists that a large magnitude noise vector may add to the transmitted vector. Accordingly, a noise vector N shown in FIG. 1B represents one of an infinite number of possible noise signals that may corrupt the transmitted vector (shown in phantom). The resulting received vector is shown at Z.sub.0.
The receiver quantizes the received signal to define the coordinates of the received vector. In FIG. 1B quantization is shown as having eight levels, or three bits, for each of the I and Q axes. The received vector shown in FIG. 1B may be described as having an I axis coordinate of 010 and a Q axis coordinate of 001. On the other hand, had the transmitted signal been received with only a small amount of corruption by noise, which is a slightly more probable situation since the noise follows a Gaussian distribution function, the received vector could have had an I axis coordinate of 010 and a Q axis coordinate of 010.
The soft decision problem arises from assigning a level of confidence to a decision that a particular symbol was transmitted given the fact that a specific received vector has been detected. For the example shown in FIG. 1B one may be relatively confident that a symbol of 00 was transmitted, even though a small probability exists that a large magnitude noise vector caused any of the other three possible transmitted symbols to be received with the same received vector coordinates.
For the non-differential quadrature-PSK situation described in FIG. 1B, this soft decision is not extremely complicated. The soft decision merely reflects the "closeness" of the received vector to the nearest one of the four possible transmitted vectors in a vector space, such as that shown in FIG. 1B. The quadrant number of the received vector represents a "hard decision". Using the coding scheme shown in FIG. 1B, this quadrant number is obtained by selecting the most significant bit of the I and Q coordinates of the received vector. The remaining 4 bits which describe the received vector coordinates provide extra information reflecting the quality of this hard decision. For the coding scheme shown in FIG. 1B, the greater the magnitude of the least significant 2 bits for each of the I and Q coordinates, the higher the quality, or the greater the confidence, in this hard decision. Accordingly, a soft decision data value may be supplied through proper coding of the quantization levels of a vector space.
A convolutional decoder portion of a receiver inputs this soft decision data, which is 3 bits for the I coordinate and 3 bits for the Q coordinate in the example depicted in FIG. 1B, and outputs a data sequence. The data sequence output by the convolutional decoder has a very high probability of precisely equaling the data sequence which the transmitter's convolutional encoder encoded. The extra information presented to the convolutional decoder beyond the information needed to describe a hard decision helps the decoder to improve an error rate of this data sequence.
In transmitting data using non-differential quadrature-PSK, a reference phase relationship between I and Q components of the carrier must first be established before data may accurately be detected by the receiver. Thus, non-differential quadrature-PSK experiences a problem if this reference relationship is lost during the transmission of data. When this happens all data subsequent to the loss of reference will remain bad until the reference is re-established through a synchronization process. This problem is known as "cycle slip".
One solution to the problem of cycle slip uses differential encoding as opposed to non-differential encoding. In differential encoding the reference relationship between the I and Q components of the carrier is established, not through a synchronization process, but from an immediately previous, received symbol. In other words, the transmitted information is represented by a phase change in the I-Q relationship of a current symbol relative to the immediately previous symbol, where the immediately previous symbol represents the symbol which occurred in the past and is adjacent in time to the current symbol. For example, a conventional coding scheme for differential quadrature-PSK defines a counterclockwise phase change of 90.degree. as a symbol of 01, a counterclockwise phase change of 180.degree. as a symbol of 11, a counterclockwise phase change of 270.degree. as a symbol of 10, and a counterclockwise phase change of 0.degree. or 360.degree. as a symbol of 00.
In this differential scheme if an event happens which causes an error in the reference relationship, such error will affect only one subsequent symbol. Since an error in a single symbol may easily be corrected using the convolutional encoding and decoding, differential encoding may represent a more reliable scheme.
However, in transmitting the differentially encoded data both the reference symbol, which is the immediately previous symbol, and the current symbol are corrupted by noise. Furthermore, since additive Gaussian noise characterizes the corruption, the relationship between the corruption of two successive samples is statistically independent. Consequently, the uncertainty related to determining precisely what data was in fact transmitted increases.
The receiver demodulation must be modified for a differential data receiver from that of a non-differential data receiver. With differential data, a phase relationship must be established from an immediately previous symbol. Likewise, the soft decision function becomes more complicated due to the fact that the same uncertainties which affect a current symbol also affected the immediately previous symbol.